A numerical method for solving the neutrino Boltzmann equation coupled to spherically symmetric stellar core collapse

A numerical method for solving the Boltzmann equation coupled to hydrodynamic flows, a relativistic equation of state, and lepton conservation for fermion transport has been developed. Difficulties encountered in past attempts to solve the neutron Boltzmann equation in stellar cores have been overcome. In particular, the correct diffusion limit for optically thick zones has been obtained without introducing ad hoc factors in the radial transport term. Oscillations in the neutrino distribution function in optically thin zones have been avoided. New numerical techniques for the angular aberration and frequency shift terms have been developed and successfully implemented. In particular, a finite difference representation has been developed for the angular aberration term that can be used with Gaussian quadratures and Bruenn's method has been successfully generated for the frequency shift term.